Maximizing the Sum of Pairs Satisfying an Equation

Number Theory Level 4

Consider all positive integer solutions ( x i , y i ) (x_i,y_i) to

1 + 2 x + 2 2 x + 1 = y 2 1+2^x+2^{2x+1}=y^2

Find the maximum value of the sum x i + y i x_i+y_i .

This problem is based off of an old IMO problem. Good luck!


The answer is 27.

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Finn Hulse by Finn Hulse , 21, USA

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